493edt

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← 492edt493edt494edt →
Prime factorization 17 × 29
Step size 3.85792¢ 
Octave 311\493edt (1199.81¢)
Consistency limit 41
Distinct consistency limit 23

493 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 493edt or 493ed3), is a nonoctave tuning system that divides the interval of 3/1 into 493 equal parts of about 3.86 ¢ each. Each step represents a frequency ratio of 31/493, or the 493rd root of 3.

493edt is essentially equivalent to 311edo (with patent vals matching through the 43-limit), maintaining its extremely strong consistency record through to the 41-odd-limit.

Harmonics

Approximation of prime harmonics in 493edt
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) -0.19 +0.00 -0.89 -0.86 -0.20 -0.06 -1.54 -1.20 -0.18
Relative (%) -4.8 +0.0 -23.2 -22.3 -5.1 -1.6 -39.9 -31.1 -4.7
Steps
(reduced)
311
(311)
493
(0)
722
(229)
873
(380)
1076
(90)
1151
(165)
1271
(285)
1321
(335)
1407
(421)
Approximation of odd harmonics in 493edt
Harmonic 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55
Error Absolute (¢) -1.79 +0.00 -0.26 +0.02 -0.20 -1.76 -1.51 -0.06 -1.77 +0.65 -0.89 +0.98 -1.72 -1.54 +1.31 -1.09
Relative (%) -46.4 +0.0 -6.7 +0.5 -5.1 -45.5 -39.2 -1.6 -45.8 +16.9 -23.2 +25.4 -44.6 -39.9 +34.0 -28.3
Steps
(reduced)
1444
(458)
1479
(0)
1511
(32)
1541
(62)
1569
(90)
1595
(116)
1620
(141)
1644
(165)
1666
(187)
1688
(209)
1708
(229)
1728
(249)
1746
(267)
1764
(285)
1782
(303)
1798
(319)